Abstract: Thermal leptogenesis induced by the CP-violating decay of a right-handed neutrino (RHN) is discussed against the background of quintessential kination, i.e., in a cosmological model where the energy density of the early Universe is assumed to be dominated by the kinetic term of a quintessence field during some epoch of its evolution. This assumption may lead to very different observational consequences compared to the case of a standard cosmology where the energy density of the Universe is dominated by radiation. We show that, depending on the choice of the temperature Tr above which kination dominates over radiation, all situations between the strong and the superweak wash-out regimes are equally viable for leptogenesis, even with the RHN Yukawa coupling fixed to provide the observed atmospheric neutrino mass scale ∼0.05 eV. For , i.e., when kination stops to dominate at a time which is not much later than when leptogenesis takes place, the efficiency of the process, defined as the ratio between the produced lepton asymmetry and the amount of CP asymmetry in the RHN decay, can be larger than in the standard scenario of radiation domination. This possibility is limited to the case when the neutrino mass scale is larger than about 0.01 eV. The superweak wash-out regime is obtained for , and includes the case when Tr is close to the nucleosynthesis temperature, ∼1 MeV. In this latter case the efficiency for leptogenesis is strongly suppressed, but can still explain the baryon asymmetry observed in the Universe when a resonant CP asymmetry of order 1 is assumed. Irrespective of Tr, we always find a sufficient window above the electroweak temperature T∼100 GeV for the sphaleron transition to thermalize, so that the lepton asymmetry can always be converted to the observed baryon asymmetry.